The space shuttle had a top orbital speed of 8000 m/s and orbited in a circular orbit approximately 320 km above the earth's surface. How long was one orbit in seconds?
To find the duration of one orbit in seconds, we need to use the formula for the circumference of a circle. The circumference of a circle can be calculated using the formula:
C = 2πr
where C is the circumference and r is the radius of the circle.
In this case, the radius r of the orbit is the sum of the Earth's radius (assuming a spherical Earth) and the altitude of the orbit. The altitude is given as 320 km, but we need to convert it to meters.
1 km = 1000 m
So, 320 km is equal to 320,000 meters.
The Earth's radius is approximately 6,371 km, which is 6,371,000 meters.
Now, we can calculate the radius of the orbit:
r = Earth's radius + altitude
= 6,371,000 + 320,000
= 6,691,000 meters
Next, we can substitute the value of the radius into the circumference formula:
C = 2πr
= 2π(6,691,000)
≈ 42,004,746 meters
Now, to find the duration of one orbit in seconds, we can divide the circumference by the speed of the space shuttle:
Time = Circumference / Speed
= 42,004,746 / 8000
≈ 5250.59 seconds (rounded to two decimal places)
Therefore, one orbit of the space shuttle in this circular orbit approximately 320 km above Earth's surface would take about 5250.59 seconds.